Probably, the best position to see the whole city is the castle/fortress on top of the hill which will be the first sight that will amaze you when you approach the centrum or Alstadt - the old city.

Said to be one of the largest medieval castle in the whole of europe. It's the most visible sight when you're in Salzburg. I opt to take the funicular railway going up, well, I tried to walk but the steps are too many and am a bit tired from getting lost walking.

The fare is EUR10 going up and down the funicular including the entry to the castle.

There's a collection of military stuff - guns uniforms, bullets, armories, etc... it became a military outpost during the 19th century.

The castle is huge and the inside have nothing much actually compared to other castles I've seen in France and Germany, in fact I felt there're more tourism business inside the castle (souvenir shops) than exhibits. But the view of the whole city on the terraces of the castle are marvelous, kind of resfreshing. You can see the whole city and the long winding river. Something that you shouldn't miss when you're in Salzburg.